Solve for $x$ and $y$ using elimination. ${-x-4y = -21}$ ${x-3y = -7}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-7y = -28$ $\dfrac{-7y}{{-7}} = \dfrac{-28}{{-7}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x-4y = -21}\thinspace$ to find $x$ ${-x - 4}{(4)}{= -21}$ $-x-16 = -21$ $-x-16{+16} = -21{+16}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 4}$ into $\thinspace {x-3y = -7}\thinspace$ and get the same answer for $x$ : ${x - 3}{(4)}{= -7}$ ${x = 5}$